# NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

**NCERT solutions for class 8 maths chapter 10 Visualizing Solid Shapes- ** You have already learnt about the 2D geometry in which basic shapes like a circle, a rectangle, square or rhombus are measured by length and width. We live in a 3-Dimensional world where every object that we can see or touch has three dimensions length, width, and height. For example, the room can be described by 3-dimensions length, width, and height. In this article, you will get NCERT solutions for class 8 maths chapter 10 visualizing solid shapes that are prepared and explained in a detailed manner to clear your doubts. In this chapter, you will study solid objects like cubes, cuboids, cones, spheres, hemispheres, etc. You must have noticed that 3-dimensional objects look different when you look from different positions or different angles. To simplify its study there are defined viewpoints (front view, side view, top view) for the 3D object.

In NCERT solutions for class 8 maths chapter 10 visualizing solid shapes, maximum questions are related to finding front view, side view, and top view of the 3D geometry. Important topics like views of 3D shapes, mapping space around us, faces, edges, and vertices of the objects are covered in this chapter. NCERT solutions for class 8 maths chapter 10 visualizing solid shapes are very helpful in engineering drawing, locating the place and will build a basic understanding of the 3D shapes. You can find NCERT solutions from class 6 to 12 by clicking on the above link. Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

Let's understand this chapter with the help of an example of a brick with its front view, side view, top view.

You can visualize a few more shapes your self.

For example: Take a cylinder. What is the side view of it? Is circular? Now take bangles of the same size and hold them together. Is it looks like a cylinder?

from the above-mentioned activity, we observed that when we hold a few bangles which are circular in shape with small thicknesses together we obtained a hollow cylinder.

** Important topics of NCERT Class 8 Maths Chapter 10 Visualizing Solid Shapes- **

- 10.1 Introduction
- 10.2 Views of 3D-Shapes
- 10.3 Mapping Space Around Us
- 10.4 Faces, Edges, and Vertices

** NCERT Solutions to the exercises of Class 8 Maths- Visualizing Solid Shapes **

** NCERT solutions for class 8 maths chapter 10 visualizing solid shapes topic 10.1 introduction **

** Question:1 ** Match the following: (First one is done for you)

** Answer: **

Matched items are:

** Question:2 ** Match the following pictures (objects) with their shapes:

| | |
---|---|---|

(i) An agricultural field |
| Two rectangular cross paths inside a rectangular park. |

(ii) A groove |
| A circular path around a circular ground. |

(iii) A toy |
| A triangular field adjoining a square field. |

(iv) A circular park |
| A cone taken out of a cylinder. |

(v) A cross path |
| A hemisphere surmounted on a cone. |

** Answer: **

Matched objects are:

** NCERT solutions for class 8 chapter 10 visualizing solid shapes-Exercise: 10.1 **

** Object Side view Top view **

** Answer: **

Matched objects are:

(1) →iii)→iv)

(2) →i) →v)

(3) →iv)→ii)

(4) →v) →iii)

(5) →ii) →i)

** Question:2(a) ** For each of the given solid, the three views are given. Identify for each solid the corresponding top,

front and side views.

** Answer: **

(a) Different views have given: ** (i) Front, (ii) Side, (iii) Top. **

** Question:2(b) ** For each of the given solid, the three views are given. Identify for each solid the corresponding top,

front and side views.

** Answer: **

** (b) (i) Side view, (ii) Front view, (iii) Top view. **

** Question:2(c) ** For each of the given solid, the three views are given. Identify for each solid the corresponding top,

front and side views.

** Answer: **

** (c) (i) Front view, (ii) Side view, and (iii) Top view. **

** Question:2(d) ** For each of the given solid, the three views are given. Identify for each solid the corresponding top,

front and side views.

** Answer: **

** (d) (i) Front view, (ii) Side view, and (iii) Top view. **

** Question:3(a) ** For each given solid, identify the top view, front view and side view.

** Answer: **

** (a) (i) Top view, (ii) Front/ Side view, and (iii) Side/ Front view. **

** Question:3(b) ** For each given solid, identify the top view, front view and side view.

** Answer: **

** (b) (i) Side view, (ii) Front view, and (iii) Top view. **

** Question:3(c) ** For each given solid, identify the top view, front view and side view.

** Answer: **

** (c) (i) Top view, (ii) Side view, and (iii) Front view. **

** Question:3(d) ** For each given solid, identify the top view, front view and side view.

** Answer: **

** (d) (i) Side view, (ii) Front view, and (iii) Top view. **

** Question:3(e) ** For each given solid, identify the top view, front view and side view.

** Answer: **

** (e) (i) Front view, (ii) Top view, and (iii) Side view. **

** Question:4(a) ** Draw the front view, side view and top view of the given objects.

** Answer: **

** The front view, top view, and side view of a tent are shown below: **

** Question:4(b) ** Draw the front view, side view and top view of the given objects.

** Answer: **

** Front view, Top view, and Side view of the table shown below: **

** Question:4(c) ** Draw the front view, side view and top view of the given objects.

** Answer: **

** The front, top, and side views of the nut are: **

** Question:4(d) ** Draw the front view, side view and top view of the given objects.

** Answer: **

The front view, side view and top view of the hexagonal block are shown below:

** Question:4(e) ** Draw the front view, side view and top view of the given objects.

** Answer: **

** The front view, side view and top view of the dice as shown below: **

** Question:4(f) ** Draw the front view, side view and top view of the given objects.

** Answer: **

** The front view, side view and top view of the given solid. **

** NCERT solutions for class 8 maths chapter 10 visualizing solid shapes-Exercise: 10.2 **

** Question:1(a) ** Look at the given map of a city.

** Answer: **

(a) Coloured map shown:

** Question:1(b) ** Look at the given map of a city.

** Answer: **

(b) marked points of intersections "X" and "Y":

** Question:1(c) ** Look at the given map of a city.

In red, draw a short street route from Library to the bus depot.

** Answer: **

Route from Library to bus depot is shown:

** Question:1(d) ** Look at the given map of a city.

Which is further east, the city park or the market?

** Answer: **

(d) The ** city park ** is further east.

** Question:1(e) ** Look at the given map of a city.

Which is further south, the primary school or the Sr. Secondary School?

** Answer: **

** (e) Sr. Secondary School ** is further south.

** Question:2 ** Draw a map of your class room using proper scale and symbols for different objects.

** Answer: **

** Do it yourself. **

** Answer: **

** Do it with your own imagination. **

** Question:4 ** Draw a map giving instructions to your friend so that she reaches your house without any difficulty.

** Answer: **

** Do it with your own imagination. **

** NCERT solutions for class 8 maths chapter 10 visualizing solid shapes topic 10.4 faces, edges and vertices **

** Answer: **

Cuboid | 6 | 8 | 12 | 14 | 14 |

Triangular pyramid | 4 | 4 | 6 | 8 | 8 |

Triangular prism | 5 | 6 | 9 | 11 | 11 |

Pyramid with square base | 5 | 5 | 8 | 10 | 10 |

Prism with square base | 6 | 8 | 12 | 14 | 14 |

Solid | F | V | E | F+V | E+2 |
---|

** NCERT solutions for class 8 maths chapter 10 visualizing solid shapes-Exercise: 10.3 **

** Question:1(i) ** Can a polyhedron have for its faces

** Answer: **

** (i) ** No, a ** polyhedron ** cannot ** have 3 triangles ** for ** its faces ** .

** Question:1(ii) ** Can a polyhedron have for its faces

** Answer: **

(ii) Yes, a ** polyhedron having 4 ** ** triangles is ** pyramid on ** triangular ** base.

** Question:1(iii) ** Can a polyhedron have for its faces

** Answer: **

(iii) Yes, a ** polyhedron ** can have ** faces ** of a square and four ** triangles ** which makes a pyramid on square base.

** Question:2 ** Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid).

** Answer: **

** Yes ** , it is possible if the number of faces is four or more than four.

** Question:3(ii) ** Which are prisms among the following?

** Answer: **

(ii) The unsharpened pencil is a prism.

** Question:4(i) ** How are prisms and cylinders alike?

** Answer: **

(i) A prism is a polyhedron whose base and top are congruent polygons and whose other faces, i.e., lateral faces are parallelograms in shape. Also, the cylinder has base on top and bottom and faces are parallel.

** Question:5 ** Is a square prism same as a cube? Explain.

** Answer: **

** No ** , not always, because it can be a cuboid also when extended.

** Question:6(i) ** Verify Euler’s formula for these solids.

** Answer: **

(i) Euler formula ** F+V = E + 2. **

So, Number of faces (F) = 7, Number of vertices (V) = 10 and number of edges (E) = 15.

Hence putting in the formula; we get,

7 + 10 = 15 + 2

17 = 17 hence, ** it satisfies the Euler formula. **

** Question:6(ii) ** Verify Euler’s formula for these solids.

** Answer: **

(ii) Euler formula ** F+V = E + 2. **

So, Number of faces (F) = 9, Number of vertices (V) = 9 and number of edges (E) = 16.

Hence putting in the formula; we get,

9 + 9 = 16 + 2

18 = 18 hence, ** it satisfies the Euler formula. **

** Question:7 ** Using Euler’s formula find the unknown.

** Answer: **

We know the Euler Formula:

** F + V = E + 2 ** :

hence we can easily find the unknown let say ** 'F, V, and E' **

** So, For Ist case: **

F + 6 = 12 + 2 or ** F = 8, hence the number of faces in Ist case is 8. **

** For IInd Case; **

5 + V = 9 + 2 or ** V = 6, hence the number of vertices in IInd case is 6. **

** For IIIrd case; **

** 20 + 12 = E + 2 or E = 30, hence the number of Edges in the IIIrd case is 30. **

| 8 | 5 | 20 |

| 6 | 6 | 12 |

| 12 | 9 | 30 |

** Question:8 ** Can a polyhedron have 10 faces, 20 edges and 15 vertices?

** Answer: **

Checking using Euler's Formula:

F + V = E +2;

Given that F = 10, V = 15 and E = 20 so,

Putting in equation: 10 + 15 = 35 and 20 +2 = 22

** Hence, given polyhedron having 10 faces, 20 edges and 15 vertices is not possible. **

** NCERT solutions for class 8 maths: Chapter-wise **

** NCERT solutions for class 8: Subject-wise **

In NCERT solutions for class 8 maths chapter 10 visualizing solid shapes only one formula has been used know as Euler’s formula.

For any polyhedron-

where F - Number of faces

V - Number of vertices

E - Number of edges

As the name suggests this chapter is more about visualizing the shapes and drawing the front view, side view, and top view. In exercise 1 and 2 of NCERT solutions for class 8 maths chapter 10 visualizing solid shapes, most questions are related to visualizing shape and mapping which are explained with the help of drawing and graphs.

** Happy Reading!!! **

## Frequently Asked Question (FAQs) - NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

**Question: **What are the important topics of chapter Visualizing Solid Shapes ?

**Answer: **

Views of the 3D-shapes, faces, edges and vertices are the important topics of this chapter.

**Question: **How many chapters are there in the CBSE class 8 maths ?

**Answer: **

There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.

**Question: **Does CBSE provide NCERT solution for class 8 ?

**Answer: **

No, CBSE doesn't provide NCERT solutions for any class and subject.

**Question: **Where can I find the complete solutions of NCERT for class 8 ?

**Answer: **

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

**Question: **Where can I find the complete solutions of NCERT for class 8 maths ?

**Answer: **

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

**Question: **How does the NCERT solutions are helpful ?

**Answer: **

NCERT solutions are provided in a very detailed manner so it will give the conceptual clarity to students as well it helps them in their homework.

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